Approximate Green's Function for Surface Foundations

In a strength‐of‐materials approach to foundation dynamics, approximate Green's functions are employed in lieu of rigorous fundamental solutions. For a vertical point load on the elastic half‐space, the form of the Green's function may be deduced via nonmathematical physical reasoning, then calibrated with a few constants taken from rigorous solutions. By superposing point loads, approximate Green's functions are constructed for a ring, then a disk. Finally, arbitrarily shaped foundations are treated as an assemblage of subdisks. As an example, rectangular foundations with various slenderness ratios are analyzed. The results verify that for slenderness ratios $a/b<4$, rectangular foundations may be replaced by equivalent disks. For vertical motion, the equivalent disk has the same area as the rectangular foundation. For rocking motion the equivalent disk has the same area moment of inertia about the axis of rotation. To account for the increased stiffness of rectangular foundations (corner‐punching effect), the spring coefficients of the equivalent disks are increased slightly; the appropriate correction factors are presented graphically.